Detecting time-irreversibility in multiscale systems: correlation and response functions in the Lorenz96 model

TL;DR

This study investigates the nonequilibrium properties of the Lorenz96 multiscale model by analyzing correlation functions and responses, revealing insights into time-reversal symmetry breaking and energy transport across scales.

Contribution

It introduces a novel analysis of the Lorenz96 model using higher-order correlations and response functions to characterize its nonequilibrium behavior and transport properties.

Findings

Correlation functions detect time-reversal symmetry breaking.

Energy perturbations transfer differently across scales.

Response to perturbations depends on the protocol used.

Abstract

Due to their relevance to geophysical systems, the investigation of multiscale systems through the lens of statistical mechanics has gained popularity in recent years. The aim of our work is the characterization of the nonequilibrium properties of the well-known two-scales Lorenz96 model, a dynamical system much used for testing ideas in geophysics, by studying either higher-order correlation functions or response to external perturbations of the energy. These tools in both equilibrium (inviscid) or non-equilibrium (viscous) systems provide clear evidence of their suitability for detecting time-reversal symmetry breaking and for characterizing transport properties also in this class of models. In particular, we characterize how localized energy perturbations are transported between the different scales, highlighting that perturbations of synoptic variables greatly impact advective variables but perturbations of the latter have a practically negligible effect on synoptic scales. Finally, we show that responses of global observables to finite size perturbations strongly depend on the perturbation protocol. This prevents the physical understanding of the system from observations of the relaxation process alone, a fact often overlooked.